The Chapman-Kolmogorov Relation : Introductory video
Before watching the video read the questions below. As you watch the video try to answer them
Questions
- Explain what the Chapman-Kolmogorov relation can be used to compute.
- Explain how the probability that $P(T_3=b \wedge T_2=c | T_1=a )$ is computed from elements of the 1-step transition probablity matrix and the justification for calculating this quantity in this way.
- Hence, explain how the probability that $P(T_3=b| T_1=a )$ is computed from the elements of the 1-step transition probability matrix and the justication for calculating this quantity in this way.
- Give a statement of the Chapman-Kolmogorov relation
- Give what you have learnt in this video write an expression for the conditional probability $P(T=4=a | T_1=a)$ using summation notation. Hint: there will be two summation signs in your expression.
- Explain what the Chapman-Kolmogorov relation can be used to compute.
- Explain how the probability that $P(T_3=b \wedge T_2=c | T_1=a )$ is computed from elements of the 1-step transition probablity matrix and the justification for calculating this quantity in this way.
- Hence, explain how the probability that $P(T_3=b| T_1=a )$ is computed from the elements of the 1-step transition probability matrix and the justication for calculating this quantity in this way.
- Give a statement of the Chapman-Kolmogorov relation
- Give what you have learnt in this video write an expression for the conditional probability $P(T=4=a | T_1=a)$ using summation notation. Hint: there will be two summation signs in your expression.